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I am so lost!!!!

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In Trig. class we were learning how to use trigometric Identities. I am so lost!!

She gave us a problem like this one.

sin^3 x - cos^3 x= (1 + sinx * cosx) (sinx - cosx)

Then she told us to use the reciprocal, quotient, and pythagorean indetities to symplify the equation, to where there is only 1 trig. finction left. I know how to use the identities but I do not understand how to use them to symplify and equation like this. can some1 plz help me, I am so lost!

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